Aspects of infinite dimensional ℓ-super Galilean conformal algebra

Abstract

In this work we construct a infinite dimensional ℓ-super Galilean conformal algebra, which is a generalization of the ℓ = 1 algebra found in the literature. We give a classification of central extensions, the vector field representation, the coadjoint representation and the operator product expansion of the infinite dimensional ℓ-super Galilean conformal algebra, keeping possible applications in physics and mathematics in mind.

Transposed Poisson structures on Block Lie algebras and superalgebras

“…Definition 17. For every ℓ ∈ 1 2 N, the ℓ-super Galilean conformal algebra gca(ℓ) (it seems that it first appeared in [3]) is a Lie superalgebra gca(ℓ) = gca 0 (ℓ) ⊕ gca 1 (ℓ) where gca 0 (ℓ) is generated by all L m , P k , c 1 , c 2 , and gca 1 (ℓ) is generated by all G m , H k , and the multiplication table is given by the following relations:…”

$\mathbb{Z}_2 \times \mathbb{Z}_2$ generalizations of infinite dimensional Lie superalgebra of conformal type with complete classification of central extensions

“…Such algebras were studied many years ago in mathematics [38][39][40][41] and in gravitational physics [42,43]. Recently, those algebras have attracted some interest in physics in the relations to integrable many-body systems [44], AdS/CFT correspondence and so on (see [45] for more detailed references). Therefore, Z 2 × Z 2 graded versions of such algebras may have potential applications to physical problems.…”